We continue to develop and test our mathematical models of human metabolism and body weight dynamics. We recently applied one of our models to objectively measure energy intake changes in comparison with self-reported intake changes during a 1-year weight-loss intervention with subjects randomized to low-carbohydrate versus low-fat diets. We found that self-reported changes in energy intake indicated a relatively persistent state of calorie restriction of 500 to 600 kcal/d at 3, 6, and 12 months with no significant differences between the diets. However, the objective model-based estimates of energy intake change demonstrated large early decreases in calorie intake > 800 kcal/d followed by an exponential return to 100 kcal/d below baseline at the end of the year. Accounting for self-reported physical activities did not materially affect the results. Discrepancies between the objective, model-based estimates of calorie intake changes and the self-reported measurements became progressively greater over time. Our results indicated that instructions to follow the low-carbohydrate diet resulted in greater calorie restriction than the low-fat diet in the early phases of the intervention, but these diet differences were not sustained. We also recently modeled the potential role of so-called protein leverage on US obesity prevalence whereby decreasing the protein fraction of the food supply leads to compensatory increases in total energy intake in an attempt to maintain a target amount of absolute protein consumed. According to food balance sheets published by the Food and Agriculture Organization of the United Nations, while the absolute protein content of the US food supply has increased since the early 1970s, the fraction of available calories from protein has decreased by 1% because of greater increases in available carbohydrate and fat. Our mathematical model indicated that even such a small decrease in the protein fraction of the food supply has the potential to result in relatively large increases in energy intake according to the protein leverage model. Therefore, while the protein leverage effect is unlikely to fully explain the obesity epidemic, its potential contribution should not be ignored. Finally, we extended our mathematical model of childhood growth to simulate the energy balance dynamics from birth through adulthood and applied our model to estimate the potential effect on infant body weight and adiposity of inaccurately measured infant formula.